* Opened with teachers properly assigned to various buildings, unlike the chaos and strike threat of last September's opening.

* Found itself run by what many feel is the most informed and responsible school committee in years.

* Taken steps to unravel its eight-year-old court-ordered desegration plan, which federal court Judge W. Arthur Garrity Jr. is preparing to hand over to local control.

* Designed a uniform curriculum, which allows students who must transfer between schools to keep pace with their work.

Now, in rapid-fire succession, three more feathers have been stuck in the school cap:

The business community announced a detailed and carefully written bargain with the schools. Known as the Boston Compact, it says, in effect, that if the schools improve the quality of their students, local businesses will agree to hire them.

Mayor Kevin H. White made his first public speech on the schools in years. Long accused of ignoring the problem, he has now offered to help improve the image of the schools.

And on Sept. 29 the Boston-based Bank of New England, applauding what its president called ''the new spirit of cooperation,'' put its money where its mouth is. It announced plans to fund nine $6,500 excellence-in-teaching awards during each of the next five years - the largest such awards in the nation, and an unprecedented move for the bank.

The $300,000-plus package focuses on what observers agree is a critical issue in the schools: teacher morale.''We realize that money is not what motivates teachers,'' said bank president Roderick M. MacDougall, who conceived of the plan to provide ''tangible'' evidence of appreciation. But he added that ''very little can be accomplished in the schools without the enthusiastic support of the teachers,'' and noted that ''we want them to know that they're important and critical to the process.''

Superintendent Robert R. Spillane calls the Teacher Excellence Award Program ''a nationally significant example'' and ''the single most striking program yet designed'' between the business community and the Boston schools. The nine $6, 500 awards - which the National Education Association says are unique in the country for the size and number of the grants - will give new meaning to the ongoing ''Teacher of the Year'' program, which currently rewards classroom teaching in each of the city's nine school districts. Since each recipient can win the honor only once, the awards will go to 45 teachers in the next five years.

Over the past year, Boston's top-level business and community leaders have engaged in considerable discussion about how to improve the city's social and economic health. Participants in these discussions have noted the frequency with which the upgrading of the schools has been cited as essential to economic improvement.

Mr. MacDougall, in effect, seemed to confirm that thesis. Asked by journalists how the award had come about, he candidly admitted to a certain ''self-interest'' on the part of the bank. ''Our survival as an institution depends on the economic health of the City of Boston,'' he said, noting that the schools played a major part in supplying new employees and allowing current employees to educate their children.

He said that he purposely kept the bank's name out of the title of the award, hoping that other corporations might also contribute.